We investigate how the [O II] properties and the morphologies of galaxies in clusters and groups at z = 0.4-0.8 depend on projected local galaxy density, and compare with the field at similar redshifts and clusters at low z. In both nearby and distant clusters, higher density regions contain proportionally fewer star-forming galaxies, and the average [O II] equivalent width of star-forming galaxies is independent of local density. However, in distant clusters the average current star formation rate (SFR) in star-forming galaxies seems to peak at densities similar to 15-40 galaxies Mpc(-2). At odds with low-z results, at high z the relation between star-forming fraction and local density varies from high- to low-mass clusters. Overall, our results suggest that at high z the current star formation ( SF) activity in star-forming galaxies does not depend strongly on global or local environment, though the possible SFR peak seems at odds with this conclusion. We find that the cluster SFR normalized by cluster mass anticorrelates with mass and correlates with the star-forming fraction. These trends can be understood given (1) that the average star-forming galaxy forms about 1M(circle dot) yr(-1) (uncorrected for dust) in all clusters; (2) that the total number of galaxies scales with cluster mass; and (3) the dependence of star-forming fraction on cluster mass. We present the morphology-density ( MD) relation for our z 0.4 - 0.8 clusters, and uncover that the decline of the spiral fraction with density is entirely driven by galaxies of type Sc or later. For galaxies of a given Hubble type, we see no evidence that SF properties depend on local environment. In contrast with recent findings at low z, in our distant clusters the SF-density relation and the MD relation are equivalent, suggesting that neither of the two is more fundamental than the other.